Photovoltaic conversion of solar energy using optical concentration systems

1977

COMMISSION OF THE EUROPEAN COMMUNITIES

energy

Photovoltaic conversion of solar energy using optical concentration systems

K. KREBS

Joint Research Centre lspra Establishment - Italy

EUR 5894 EN

PHOTOVOLTAIC CONVERSION OF SOLAR ENERGY USING OPTICAL

CONCENTRATION SYSTEMS

by

K.KREBS

Euratom CCR Ispra (Va), Italy

ABSTRACT Solar radiation is the largest inexhaustible and environ­

mentally acceptable source of energy, but whereas thermodynamical­ly speaking solar energy is of high quality, it is at the same ti­me a source of low energy density. These aspects indicate the great potential but also the difficulty to use this form of energy econo­mically. Basically there are two approaches to cope with this pro­blem : development of low-cost energy converters and/or concentra­tion of the incident radiation before conversion.

In the following paper we are treating briefly the econo­mical aspect of photovoltaic converter/concentrator devices. A more detailed discussion will then be given concerning conditions which have to be fulfilled in order to make the concentration concept viable. These conditions are related to the quality of incident ra­diation, the behaviour of a photoelectric converter at high light intensities and to the availability of efficient low-cost concen­trator devices.

The analysis of problems encountered in these three areas indicates that there is no major obstacle preventing a successful exploitation of the con~ept. The final assessment of the true eco­nomic impact of this approach will depend mainly on the further de­velopment of economic high intensity solar cells. The available light quality is for many areas sufficient and (partially new) solu­tions for concentrating devices do exist. Thus the combination of low cost cells and optical concentration is a possible way to shor­ten the time to reach the break-even point for a large scale utili­zation of solar electricity, it might even be the best way to reach that goal.

RESUME

La radiation solaire est la source d 4 energie la plus im­portante, a la fois inexhaustible et acceptable du point de vue de l'environnement. Mais tandis que l'energie solaire thermodynamique­ment parlant est de haute qualite, elle est en meme temps une sour­ce de faible densite d'energie. Ces aspects montrent le grand po­tentiel mais aussi la difficulte d'utiliser cette forme d'energie economiquement. Fondamentalement il existe deux approches pour re­soudre ce probleme : developement de convertisseur d'energie a bas prix et/ou concentration du rayonnement incident avant conversion.

Dans l'article qui suit nous traitons brievement de l'as­pect economique des systemes conversion/concentration photovoltai~ ques. Une discussion plus detaillee est donnee ensuite au sujet des conditions qui doivent etre remplies de fa~on a rendre le concept

1

de concentration viable. Ces conditions sont liees a la qualite du rayonnement incident, au comportement du convertisseur photo­electrique aux hautes intensites lumineuses et a la possibilite d'utiliser des systemes de concentration efficace et bon marche.

L'analyse des problemes rencontres dans ces trois do­maines indique qu'il n•y a pas d'obstaclP majeur s'opposant a une exploitation de ce concept couronnee de succes. L'evaluation fina­le de l'impact economique reel de cette approche depend principa­lement du developement approfondi de cellules solaires economiques a haute intensite. La qualite de la lumiere disponible est suffi­sante dans de nombreuses regions et des solutions (partiellement nouvelles) pour les systemes de concentrations existent reellement. Ainsi la combinaison de cellules bon marche et de la concentration optique est un moyen possible de raccourcir le temps necessaire pour arriver au point d'equilibre pour !'utilisation sur une large echelle de l'electricite solaire. c•est peut-etre la meilleure fa~on d'atteindre a ce but.

1. INTRODUCTION

The large scale utilization of solar radiation could eventually be used to substitute to a large extent fossil fuels and even nuclear power. The time at which a transition from non-renewable energy sources to this virtually inexhaustible and environmentally attrac­tive source will make an impact depends in first place on the eco­nomics of solar energy conversion systems.

Since solar radiation is energy of high quality direct conversion to electricity is a possible and efficient process. This has been shown most clearly and since many years by its application in spa­ce technology. Now, in space there is little or no competition from other energy sources, whereas on earth the competition is enormous and especially by techniques which have been developed for long time and by big industry. On earth solar cells have proven their usefulness especially for those small energy applications where competitive energy sources have either high cost to energy ratios or where problems exist with maintenance or accessibility. Present panel costs are in the order of 20-30 t/peak watt. A look at the cost distribution of a complete panel (Fig. 1) indicates that the problem of reducing the price by two or three orders of magnitude in order to be competitive with conventional large scale electri­city producers might be a task which could be beyond our techno~o­gical possibilities for a long time. Mass production or economy of scale alone will certainly not solve this problem and even a sub­stantial improvement in large area silicon single crystal produc­tion might not be sufficient.

Since one of the main reasons for the high cost of solar energy lt~s in its low energy density a reduction of costs )ould be ex­pected from concentrating the incident radiation - 5 : The increase of energy flux on the converter would reduce the necessary solar cell area and may even lead to an improvement of the economy of scale of solar systems.

It has been stated that for very large solar power plants focusing thermal systems might offer an advantage because of their poten­tially better conversion efficiency (about 50-60% of the Carnot value). However, at least for smaller and especially for distribu­ted applications photovoltaic systems could still be the better

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choice, it is also expected that the maintenance and especially the cooling of these conceptionally simpler systems would be less ex­pensive. The decisive argument to favour one or the other version would be of course the power rate per k1lowatt-hour which could be achieved in a prototype installation.

An important advantage for solar cell/optical concentrator systems versus conventional photoelectric systems lies i) the reduction in energy pay-back time. At present one estimates 6 that the energy needed to produce a solar cell array amounts to about 3000 k~.rhjm2. Thus one would need about 20 years of operation at an average in­put of 4 kWhjm2d to recover the energy which was needed to produce that panel : At 5 c/kWh the cost for this energy corresponds even so to only about 5% of the actual panel price. Since the energy to produce concentrators can be much smaller, substantial energy sa­vings could be expected if one would use the concentration concept.

Under certain assumptions on converter behaviour, incident radia­tion, money cost etc., one can estimate the economic impact of this concept on specific energy costs (Fig. 2). One sees that- depen­ding on the cost per converter area - low, medium or high concen­tration factors will be necessary to meet certain objectives.

However, the concentration approach could become a viable solution only if a number of necessary conditions are fulfilled : (1) the incident radiation must be of sufficient quality, (2) the photo­electric system must be able to work efficiently at high light in­tensities and (3) one has to find economic optical systems which concentrate the radiation from a time and position variable source. The following sections are mainly concerned with a discussion of these ~onditions, they are partially based on a more detailed re­port 7J, which will contain also results of experimental work done at Ispra.

2. INCIDENT RADIATION

The incident radiation should be of a quality useful to concentra­tors, i.e. the direct component (HDIR) must be sufficiently inten­se. Its value determines the necessary minimum concentration ratio of the system. Assuming that the concentrator works only with di­rect light, then we would observe a net energy gain if CRth)HTOT/ HDIR, where CRth is the theoretical concentration ratio of a given system. The rat1o HDIR/HTOT determines also the effective CR which is observed for a given light composition and a given CTth'

CR =- HTOT( c) eff- 11IOT(R)

C HDIR.{R) HDIF(R) R.th HTOT(R) + DR HTOT(R) ( 1 )

(C : concentrator, R : reference, DR : fraction of diffuse light accepted by the concentrator). If no measurements of direct (or diffuse) radiation or Qf sunshine duration are available, the Liu­jordan approximation BJ might be used to obtain HDIR/HTOT :

HDIR = A _ i--IDIF ~ 1 HTOT HTOT

HTOT -HO J (2)

where HO is the radiation on a horizontal surface in absence of an atmosphere. Fig. 3 shows measurements taken at Ispra ( ~= 45.8°N)

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which confirm that relation. In a 10y (monthly) average (1962-1972) HTOT/HO was 0.46 at that station. For the same time period the rela­tive sunshine duration was 0.5. Thus in Ispra only systems with CRth> 2 could in principle offer an advantage on a yearly basis. Since in general also some part of the diffuse radiation will be accepted by a concentration system, this CR-limit may be correspon­dingly smaller, on the other hand, one should be aware of the addi­tional cost of the concentrator.

A large part of the world will have HDIR/HTOT - ratios between 0.4 and 0.8 : for all those areas the incident radiation would thus be of sufficient quality if the CR-values would be chosen above about 1 • 3 to 2. 5.

3. THE PHOTOVOLTAIC CONVERTER The solar cell should be able to convert incident radiation of in­creased energy density not only effectively but also economically into electricity. The increase in flux level gives rise to two main difficulties : higher intensities mean higher cell temperatures and increased currents. Both have a negative influence on the conver­sion efficiency and may thus invalidate the whole concept. The I-V characteristic of a n-p junction is usually written as

(3)

The open circuit voltage and short circuit current density are then

(4)

and ~,

Jsc = - JL = - e f G(A) N(A) d). (5) 0

(JL : light.ge~erated current density, O(~) : collection efficien­cy, N(~) : 1nc1dent spectrum,~,= hc/~E, ~E: energy gap). With these terms the conversion efficiency becomes

~ = C.F ) (6)

where the curve factor is defined as rF - J V /J V ~ - m m sc oc ·

(Jm' Vm : current density and voltage at optimum working point, Pin : incident power density).

If we neglect for a moment temperature and series resistance ef­fects, we see that V

0 increases logarithmically with J • This

leads to an increase tn conversion efficiency with conc~ntration and follows also from the thermodynamic reason 9) that concentra­ted ~adiati~n i~ basically of higher (Carnot) quality. ~or conceQ­trat1on rat1os 1n the orrler of 1000 one expects theoret1cally 10)

8

an increase in efficiency by 30 to 40%.

3.1. Temperature Effect

An increase in temperature influences mainly the open ~ircuit vol­tage and there the main effect is due to an increase in the reverse saturation current density

J = CT3 exp (- AE) [i_( PL)I/:2.. + j_ (.P!L )1/2..] ( 7) o k T N0 -r.f=> NA Tn

If we consider two temperatures T and T the corresponding open cifcuit voltages at constant short circuft current are related by 11 )

V2.. = ~ _ r _ ~ ) r,_ _ 3 kT .en r,_ + .i. ( ~ (t _ t) l e.E \1 AE ~ eAE T, A~ dT 2. 11) ) ( 8)

which indicates the usually observed approximatively linear decrea­se of V

0c with T. One observes also that semiconductors with a lar­

g~r energy gap show a relatively slower decrease of v0

c with incre~ s1ng temperature.

If we now neglect other (and in general smaller) temperature ef­fects (e.g~ on J ) the converst,on efficiency will also be a lir.~ar ly decreasing fun~tion of T. \~Thich temperature and thus which Yl -will be actually obtained under a give~ irradiation depends on 'the cooling properties of our system 12-15). Approximately we may wri­te (radiation losses being neglected)

( s) )

where K is the thermal conductivity per unit area (in KW m- 2K- 1),

a is th® absorptivity and p the temperature coefficient of V0

c ,

(3 ~(AE.-Vo)/To (~ 2 mV/grad). The influence of Ke on l( was shown 1mpl1c1tly 1n Flg. 2.

It is obvious that sufficient ~ooling can reduce efficiency losses to tolerable values. A very interesting)solutiun is t~~e photovoltaic-thermal (or hybrid) system 16, 17 , where the ab­sorbed heat is used as in a solar thermal panel. Since the money value of the absorbed heat is roughly of the same order as the va­lue for the electrical energy output, system costs can be reduced by a factor 2. Another special case is the solar electric pump, where the system may be constructe~ in a way that it is able to cool itself by the pumped water 18), therefore neither additional energy nor additional water is needed.

3.2. Series Resistance

The second and more critical influence on conversion efficiency and power putput of a cell is due to its finite series resistance. If the light level falling onto a photovoltaic converter is increa­sed from 1

1 to 1 2 the corresponding I-V characteristics are rela-

9

ted to each other by (taking I positive) 19 )

( 10)

and

J ( 11 )

where

t~IL = ( t~ -t1 )rl1 = ( cR-1) rL.., (12) (IL 1 : light generated current at level L1).

This means that the second I-V curve is obtained from the first one by two translations of the coordinate system by amounts - ~IL (vol­tage axis) and AI1 . R (current axis). From this procedure one may derive the behaviour Qf the power output as function of incident intensity (Fig. 4) 14J. One sees that depending on R for higher C~-values the relative gain in power output decrease~ more and mo­re, this indicates that higher concentration can be applied econo­mically only if the series resistance of the cell can be kept cor­respondingly lower. The eventual success of the concentration con­cept depends to a large extent on the possibility to achieve this goal in an economic way.

The series resistance of modern cells is determined predominantly by the resistance of the front grid and of the highly doped sur­face layer. The first improvement lies in a modification of the grid (Fig. 5) and in a modificati~8)in doping and thickness of the surface layer. It has been shown that in this way cells working under a 25-fold concentration show good I-V curves. The series re­sistance of a grided surfac~ layer varies like n-2, where n is the number of grid lines 21, 22J. !Thus the distance between lines should be chosen proportional to cR-1 2, or in other words, the unit cell must decrease in size as CR increases. Difficulties with the resi­stance of the grid itself may be avoided by means of a superimpo­sed coarser grid 12, 15). Using a suitable fine grid (90 Mm spa­cing and 4~m width)and a surface doping density of 5x1o20 cm-3 it has been possible to obtain 8% conversion efficiency at CR / 800 for silicon 15).

Another ide~, which has been exploited quite successfully with Ga As cells 11;, 23J consists in the application of a transparent con­ductive semiconductor window on top of the surface layer 24, 25J. This window acts as a resistance parallel to the surface sheet re­sistance. So far the heighest intensities have been used with p-Al GaAs /p - GaAs/n - GaAs cells : at 1735 suns and 19% effici~ncy output power densities of 24 W/cm2 have been reached 11) 23J. Materials like In2o3 might eventg~lly be used on silicon if crack­ing and peeling can be avoided 2 J. The problem with the highly doped front layer might eventually also be sol~ed by growing thick­er and less doped surface layers epitaxially. l)

The front-layer can be eliminated altogether in another concept, the vertical junction arrangement of the HI cell 28) (Fig. 6). This system has the additional advantage of being a low current series connected converter, it can be irradiated from two sides

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and due to light modulation of the conductivity there is even a decrease in series resistance with concentration. Measurements with concentration ratios up to 300 have shown that with the ver­tical structure silicon can work with hiqh CR-values similar high concentratio~ ratios have also been reached with the ~ussian Photo­volt cell 29J.

The main draw back of very high concentration cells consists (1) in their high production costs and (2) that they require more accu­rate concentrating devices. If we remember Fig. 2, one finds that high CR-values in connection with expensive converters do not lead to lower cost levels than it can be reached with silicon at modera­te concentration. This implies?of course)that indeed efficient si­licon concentrator cells could be developed, say, below 5 %/ peak watt : For medium CR-values this seems to be possible 12).

Fig. 7 sums up some of the output power densities which have been reached so far by various authors. This figure proves the princi­ple physical feasibility of the concept.

4. OPTICAL CONCENTRATION

The exploitation of the concentration concept shifts the emphasis to develop low cost cells somewhat to the problem of finding the most economical optical concentrator.

Since the light source is non-stationary and of varying intensity, one might ask what should be defined as optimum concentrator under these conditions. For a Lambert law source the irradiance of a sur­face element dF' is related to the radiant emittance of a disk li­ke sourceS into half space (1

0 : radiance of source) by(Fig. Ra)

D = d.2

E = rrL sin \r d.t d.F' 0 ( 1 3 )

Thus we would say a concentrator is "geometrically ideal", if it compensates fully for the geometrical loss, i.e. if

De = C"R. = _A_ ( 14) .D S Sit'J

10 This relation implies the sine condition of geometrical optics30 ) (Fig. 8b)

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( Yty.1o)2 = A ( 16) sin~I.Lo

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h f si.YJ u-1 (17)

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d

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(tt- ( 19)

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From these relations we obtain with the sun's half angle 6 = 16' a maximum concentration ratio of CR = 2152 = 46200, which for in­stance with CR x I

0 = (5 T s 4 leads to Ts = 5700°K ( 1

0 : solar con­

stant).

Our main aim is the optimization of the energy gain, thus not Qnly the concentration ratio but also the energy collect1on time 32) plays a part. Since we are looking for inexpensive concentrators, we limit at first our consideration to stationary or quasi-statio­nary systems. For such systems the collection time is determined by the total acceptance angle 2 J' , and cS" itself is defined not by the extension of the solar disk but by an average over the appa­rent daily solar motion across the sky. From a plot of the pro­jection angle of the solar motion in the meridional plane as fun­ction of time (Fig.9), we see that d-values between 5° and 10° lead to acceptable collection times. Of course, for linear systems this means that CR will then remain below 12.

Let us consider briefly the properties of some typical (quasi) -stationary linear systems :

a) V-Trough.

The simplest device to obtain a low concentration factor is the V-trough arrangement with two flat mirrors. We can distinguish between various types of V-concentrators by the way how one de­fines the length L of the side mirrors. In one version L is d~fi­ned by the requirement that perpendicular r~ys undergo one 33) or more 34) reflections, in another version 35J L is determined by the condition that all rays within an acceptance angle 2oshould be concentrated (Fig. 10). This last system approaches th~ ideal case (eq. (14)) if the cone angle goes to zero. Another way to meet the ide?l concentration condition is the combination with a field lens 36) (Fig. 11) : We consider this case as very promising, since it allows now to obtain even for short systems larger ideal CR­values.

b) Parabolic Trough.

The simple V-trough may be improved by using curved side mirrors. The curvature profile of the reflectors may be obtained as solu­tion of a first order differential equation for the case th~t one specifies the radiation distribution across the receiver 37J. If this distribtuion is specified in such a way that rays of a certain maximum deviation against the normal to the receiver are focused to the edges of the receiver, the profiles of the side mirrors are two inclined parabolas (Fig. 12) : this type of concentr~tor ~as therefore been called compound parabolic concentrator 32), 38). It is an ideal concentrator in the sense of eq.(14) : it concentra­tes with constant CR for the maximum possible time. One disadvan­tage of this system is the large reflector area which is needed to reach higher concentration ratios. Moreover, the non-uniform radia-

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21

tion distribution may cause difficulties if used with solar cells.

The ratio of reflec~Qr area to aperture is smaller for the classi­cal parabola 31), 3 J(Fig. 13). However, such a system stays well below the ideal concentration limit. Some disadvantage is also re­lated to the vertical motion of the focal plane with the angle of incidence.

c) Linear Fresnel Lens.

Diffraction systems have the advantage that aperture and concentra­tion area are nearly the same, thus they require less material. Moreover with Fresnel lenses such systems are relatively compact. (Fig.1~). Of course, also linear Fresnel lenses show the var1ation of focal plane for inclined rays 40) . This difficulty can be re­duced by the use of an additional v-shaped trough, cone or pyrami­dal reflector, which again - as already has been stated above -would lead to an ideal and at the same time compact system. Another possibility for an effective increase of the acceptance t1me w~th­out loss of concentration may be obtained by the addition Qf a flux redistributor around the position of the (moving) focus ?9;, 41 J.

Fig. 15 shows concentration factors for the above systems as fun­ction of acceptance angle. In Fig. ~6, we have plotted CR x (tr./tc) for the days of a year ( t !\ : acceptance time, t ~ : length of .\. ~ the day) . '· ~

So far we have mentioned only linear quasi-stat1cnary systems, which would be oriented e.g. in East-West. If h1gher CR-values are needed, one has to use concentrators (or receivers) which rotate daily at least around one horizontal, vertical or equator1al ax1s. Limitation to one axis could be combined w1th relaxation for con­centration along another axis, i.e. one would again use linear concentrators : this time, however, with much smaller 6~ and corre­spondingly higher CR-values. Fig. 17 is a sketch of such a rotati.nD sys tern. The individual concentrators are linear and the \vas te heat is used for thermal applications.

Ultimate values of concentration are obtained with true he'liosta­tic systems. A drawback of such systems mi~ht be their cost and t~e protection they need agalnst wind loading :2J. IIowever, cost re­ductions are to be expected from the development wor~ for large solar thermal power stations. In this context, costs of 34 ,tjm2 based on very large seal~ production -.have been quoted in lite­rature 43). If such 2-axls- systems w1ll have an advantage also for photovoltaic applications, depends on the requested concentra­tion factors : for silicon very high CR-values might not be necessa­ry.

5. CONCLUSION

The discussion in the foregoing chapters has shown that a success­ful application of the concentration concept will require that cer­tain conditions on incident radiation, on characteristic parameters of the photovoltaic converter and on the optical properties of the concentrator can be fulfilled. Concerning the radiation sufficient knowledge of the amount of di­rect intensity must be available, since this determines critically the minimum and the effective concentration factor. The direct com-

22

P-T

.,-M D

CR =(1/sincS){sin 2 9/2 cos b) -1

or (sin 9cos (9+b}/sinc!>)-1

f/d = (1+ cos 9) cos 9/2 sin 2 b

Figure 13

23

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Figure 14

24

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17

r-~50m

ponent may be estimated with sufficient accuracy from total hori­zontal radiation measurements using the (local)Liu-Jordan relation. Thus for many places the necessary information concerning the input can be found.

The second problem area concerns the photovoltaic converter. Where­as a few experiments indicate that silicon cells could be used for a wide range of concentration factors the economic aspects of a production of such cells still has to be investigated. For higher concentrations new designs like epitaxially grown cells or cells with window layers or very fine grids look promising. For still higher CR-values vertical junction silicon cells or III - V and II - VI cells should be investigated further. However, there is little doubt, that viable solutions can be found.

It remains the problem of the concentrator itself. For any large scale production of electricity one has to put rather stringent re­quirements on the allowable concentrator cost. Thus solutions on the basis of quasi-stationary systems or at maximum of systems with one axis rotation could have an economic advantage. Since long ac­ceptance times and not too low CR-values are desirable, too simple optical systems will probably not be the final choice. But also in this area solutions will be possible : if these solutions will be economically valid has to be verified by extended tests under real conditions.

It is obvious, that even if our analysis indicates, that there is no major obstacle which prevents a success of the concentrator con­cept, the real proof that concentrator-converter systems are pro­viding economical solutions, has to be obtained from demonstration projects of sufficient size. These alone could show that this con­cept leads really to those additional savings which probably would still be necessary even after the development of low cost solar pa­nels. Concentration and cheaper cells, e.g. of the ribbon type for linear concentrators, could then allow us to reach that ultimate goal : the break-even point for solar electricity.

REFERENCES

1. D.~.Chaoin, Introduction to the Utilization of Solar Energy ed. by A.M.Zarem and D.D.Erway, (MC Graw Hill, New York) 1963, n. 153IW.Menetry, lac. cit., o. 326

?. C.Pfeiffer, P.Schoffer, B.G.Spars and J.A.Duffie, Trans.ASME 9~A, 33 (1962) I n.schoffer and C.Pfeiffer, Trans. ASME RSA, 203 (1963) / T'.Schoffer, Proc. i8th Annual Power Conf. p~66 (1964) I W.A.Beckman and P.Schoffer, Proc. 20th Annual Power Conf. (1966) / W.A.Beckman, P.Schoffer, W.R.Hartman, Jr. and G.O.G. L~f, Solar Energy 10, 132 (1966) I W.A.Beckman, Trans. ASME 89A, 415 (1967) --

3. ?.A.Berman, Solar Energy 21, 180 (1967)

4. B.L.Ralph, Solar Energy 2Q, 67 (1966), 21, 279 (1973)

s. G.S.Daletskii, A.7.Zaitseva and L.G.Korneeva, Geliotekhnika 1• 3 (1967)

6. M.~olf, Proc. Photovoltaic Power Generation Conf., Hamburg 1966, p. 699

28

7. K.Krebs and E.Gianoli, Photoelectric conversion of Concentra-ted Solar Radiation, EURATOM Report (in preparation)

q B.Y.H.Liu and R.C.Jordan, Solar Energy 1· 1 (1960)

9. B.A.MUser, Z.Physik 148, 380 (1957)

10. F.Sterzer, RCA Review~. 316 (1975)

11. L.V.James and R.L.Moon, Con£. Record of 11th IEEE Photovoltaic Soecialists Con£., Scottsdale 1975, n. 402

12. C.E.Backus, National Science Foundation Report NSF/RANN/SE/ GI-Ll189LlJPR/7Ll/4, 1975

13. L.V.Florschuetz, Con£. Record of the 11th IEEE Photovoltaic Specialists Con£., Scottsdale 1975, o. 318

1.1. S.Deb and H.Saha, Solar Energy ~z, 67 (1975)

15. R.:r-t.Dean, L.S.Napoli and S.G.Liu, RCA R.evie~· 36, 324 (1975)

16. F.L.Vook and D.G.Schueler, Sandia Laboratories Report SAND 7Ll-0093 (1974)

17. D.G.Schueler, J.G.Fossum, E.L.Burgess and F.L.Vook, Con£. Record of 11th IEEE Photovoltaic Specialists Con£., Scottsdale 1975, p.327

18. N.S.Lidorenko, F.K.Nabiullin, E.M.Gertsik, B.V.Tarnizhevskii and Y.T.Rodinov, Geliotekhrtika ~, 20 ( 1966)

19. rvr.~7olf and H.Rauschenbach, Advanced Energy Conv. ]., -455 (1963)

20. C.A.Lewis and J.P.Kirkpatrick, Conf. Record of 8th IEEE Photo­voltaic Specialists Con£., Seattle 1970, p.123

21. M. \'701£, Proc. IRE 48, 1246 ( 1960)

22. J.Lindmayer and J.F.Allison, COMSAT Techn. Rev. }, 1 (1973)

23. L.~,·7 .James and R.L.Moon, Appl. Phys. Lett. 26, 467 (1975)

24. J.M.\~7oodall and H.J.Hovel, Appl. Phys. Lett.~. 379 (1972)

2 5. J. M. ~~roodall and H. J. Hovel, J. Vac. Sci. Techn. E, 1000 ( 197 5)

26. S.V.Lai, S.L.Franz, G.Kent, R.L.Anderson, J.K.Clifton and J.V.Masi, Con£. Record of the 11th IEEE Photovoltaic Specia­lists Conf., Scottsdale 1975, p. 399

27. V.J.Dalal, H.Kressel and P.H.Robinson, J.Appl. Phys. 46, 1283 (1975) / H.Kressel, P.Robinson, S.H.McFarlane, R.V.D'Alello and V.L.Dalal, Appl. Phys. Lett. 25, 197 (1974)

28. B.Sater and C.Goradia, con£. Record of the 11th IEEE Photo­voltaic Specialists Con£., Scottsdale 1975, p. 356

29

29. V.A.Baum, A.P.Landsman, B.A.Bazarov and D.S.Strebkov, Proc. UNESCO Congress "The Sun in the Service of Mankind", Section : Photovoltaic Power and its Applications in Space and on Earth, Paris 1973, p. 519

30. M.Born and E.Wolf, Principles of Optics, Pergamon Press, Oxford 1964, p. 167

31. W.A.Baum and J.D.Strong, Solar Energy~· 37 (195A)

32. R.r,rinston, Solar Energy .2..§_, 89 (197Li)

33. K.G.T. Hollands, Solar Energy 21· 1Li9 (1971)

3A. H.Durand, ].Michel, J.J.Hunziger and C.Hily, Proc. COMPLES International Meeting, Dhahran 1975

35. A.Rabl, Argonne National Laboratory Solar Energy Group, Report SOL 7 5-02, 197 5

36. D.R.~~'illiamson, J. Opt. Soc. Am. 1!2, 712 (1952)

37. D.G.Burkhard and D.L.Shealy, Solar Energy 2Z· 221 (1975)

38. R. '.Arins ton and H. Hin terberger, Solar Energy 2.Z, 2 55 ( 197 5)

39. H.Tabor, Solar Energy~· 27 (195A)

40. D.T.Nelson, D.L.Evans and R.K.Bansal, Solar Energy 2l• 285 ( 197 5)

41. P.E.Glaser, M.M.Chen and J.Berkowitz-Mattuck, Solar Bnergy z, 12 (1963), Applied Optics~. 265 (1963)

42. C.E.Backus, J.Vac. Sci. Technol. 23, 1032 (1975)

43. C.R.Easto~, R.W.Hallet, S.Gronich and R.L.Gervais, Proc. 9th Intersociety Energy Conversion Fngineering Con£., San Fran­zisko 1974, p. 271.

30

FIGURE CAPTIONS

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

1 •

2.

3.

4.

5.

6.

7.

R.

9.

10.

1 1 •

1 2.

1 3 •

14.

1 5.

1 6.

1 7.

Present and possible future cost distribution of photo­voltaic energy conversion systems.

Estimation of energy cost in c/kWh of various photoelec­tric concentration systems for a typical set of input pa­rameters.

a) Daily diffuse and daily total radiation, b) relative sunshine duration and monthly averages of daily diffuse/ total and daily total/extraterrestrial radiation.

Power output as function of incident intensity.

Solar cell structures. A : conventional cell, B : cell with high intensity grid and modified front layer.

Solar cell structures. C : window layer cell, D : vertical junction HI cell.

Power output densities as function of light input. Points correspond to measurements by various authors.

Optimum concentration ratio : a) irradiance at distance R from source S, b) sine condition of ray optics, c) sine condition for imaging systems with object at in­finity.

Projection angle r in function of hours from noon for various days in the year. The dashed line indicates an example for the acceptance time of a concentrator with total acceptance angle 2 cf.

V-trough concentrator with cone angle 2 9.

V-trough concentrator with Fresnel field lens.

Compound parabolic concentrator.

Parabolic trough concentrator with rim angle 9.

Linear Fresnel lens concentrator (in "collimator" mounting).

Concentration factors as function of acceptance time for various linear devices.

Concentration factor x relative acceptance time for va­rious linear systems as function of date.

Sketch of a photovoltaic-thermal converter system.

31

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